A new k-space method for simulation of ultrasonic propagation in tissue

Abstract

A new k-space method for large-scale computations of ultrasonic propagation is presented. In the new method, spatial derivatives from the second-order acoustic wave equation for inhomogeneous media are evaluated by Fourier transformation. Solutions are advanced in time using a k−t space Green’s function. Computational results indicate that the new method shares advantages of both past k-space and pseudospectral methods. For scatterers with properties similar to soft tissue, the k-space method provides much higher accuracy and lower computational cost than a 2–4 finite-difference time domain method. The k-space method also allows high accuracy to be obtained for time steps much larger than those required by a leapfrog pseudospectral method. The low dispersion inherent to the k-space method is illustrated by large-scale quasi-one-dimensional computations, in which pulse waveforms incur negligible shape change for propagation distances as large as 1000 wavelengths. Example applications of the k-space method are demonstrated, including simulation of propagation through a large-scale tissue cross-sectional model and incorporation of a k-space solver into a nonlinear inverse scattering method employing eigenfunctions of the far-field scattering operator.